The escape transition of a polymer mushroom (a flexible chain grafted to a flat non-adsorbing substrate surface in a good solvent) occurs when the polymer is compressed by a cylindrical piston of radius $R$, that by far exceeds the chain gyration rad
ius. At this transition, the chain conformation abruptly changes from a two-dimensional self-avoiding walk of blobs (of diameter $H$, the height of the piston above the substrate) to a flower conformation, i.e. stretched almost one-dimensional string of blobs (with end-to-end distance $approx R$) and an escaped part of the chain, the crown, outside the piston. The extension of this problem to the case of star polymers with $f$ arms is considered, assuming that the center of the star is grafted to the substrate. The question is considered whether under compression the arms escape all together, or whether there occurs an arm by arm escape under increasing compression. Both self-consistent field calculations and Molecular Dynamics simulations are found to favor the latter scenario.
The free energy cost of confining a star polymer where $f$ flexible polymer chains containing $N$ monomeric units are tethered to a central unit in a slit with two parallel repulsive walls a distance $D$ apart is considered, for good solvent conditio
ns. Also the parallel and perpendicular components of the gyration radius of the star polymer, and the monomer density profile across the slit are obtained. Theoretical descriptions via Flory theory and scaling treatments are outlined, and compared to numerical self-consistent field calculations (applying the Scheutjens-Fleer lattice theory) and to Molecular Dynamics results for a bead-spring model. It is shown that Flory theory and self-consistent field (SCF) theory yield the correct scaling of the parallel linear dimension of the star with $N$, $f$ and $D$, but cannot be used for estimating the free energy cost reliably. We demonstrate that the same problem occurs already for the confinement of chains in cylindrical tubes. We also briefly discuss the problem of a free or grafted star polymer interacting with a single wall, and show that the dependence of confining force on the functionality of the star is different for a star confined in a nanoslit and a star interacting with a single wall, which is due to the absence of a symmetry plane in the latter case.
By employing monomer-resolved computer simulations and analytical considerations based on polymer scaling theory, we analyze the conformations and interactions of multiarm star polymers strongly adsorbed on a smooth, two-dimensional plane. We find a
stronger stretching of the arms as well as a stronger repulsive, effective interaction than in the three dimensional case. In particular, the star size scales with the number of arms $f$ as $sim f^{1/4}$ and the effective interaction as $sim f^{2}$, as opposed to $sim f^{1/5}$ and $sim f^{3/2}$, respectively, in three dimensions. Our results demonstrate the dramatic effect that geometric confinement can have on the effective interactions and the subsequent correlations of soft colloids in general, for which the conformation can be altered as a result of geometrical constraints imposed on them.
Integral equation theory is applied to a coarse-grained model of water to study potential of mean force between hydrophobic solutes. Theory is shown to be in good agreement with the available simulation data for methane-methane and fullerene-fulleren
e potential of mean force in water; the potential of mean force is also decomposed into its entropic and enthalpic contributions. Mode coupling theory is employed to compute self-diffusion coefficient of water, as well as diffusion coefficient of a dilute hydrophobic solute; good agreement with molecular dynamics simulation results is found.
A self-consistent field theory study of lock and key type interactions between sterically stabilized colloids in polymer solution is performed. Both the key particle and the lock cavity are assumed to have cylindrical shape, and their surfaces are un
iformly grafted with polymer chains. The lock-key potential of mean force is computed for various model parameters, such as length of free and grafted chains, lock and key size matching, free chain volume fraction, grafting density, and various enthalpic interactions present in the system. The lock-key interaction is found to be highly tunable, which is important in the rapidly developing field of particle self-assembly.
The absorption of free linear chains in a polymer brush was studied with respect to chain size $L$ and compatibility $chi$ with the brush by means of Monte Carlo (MC) simulations and Density Functional Theory (DFT) / Self-Consistent Field Theory (SCF
T) at both moderate, $sigma_g = 0.25$, and high, $sigma_g = 1.00$, grafting densities using a bead-spring model. Different concentrations of the free chains $0.0625 le phi_o le 0.375$ are examined. Contrary to the case of $chi = 0$ when all species are almost completely ejected by the polymer brush irrespective of their length $L$, for $chi < 0$ we find that the degree of absorption (absorbed amount) $Gamma(L)$ undergoes a sharp crossover from weak to strong ($approx 100%$) absorption, discriminating between oligomers, $1le Lle 8$, and longer chains. For a moderately dense brush, $sigma_g = 0.25$, the longer species, $L > 8$, populate predominantly the deep inner part of the brush whereas in a dense brush $sigma_g = 1.00$ they penetrate into the fluffy tail of the dense brush only. Gyration radius $R_g$ and end-to-end distance $R_e$ of absorbed chains thereby scale with length $L$ as free polymers in the bulk. Using both MC and DFT/SCFT methods for brushes of different chain length $32 le N le 256$, we demonstrate the existence of unique {em critical} value of compatibility $chi = chi^{c}<0$. For $chi^{c}(phi_o)$ the energy of free chains attains the {em same} value, irrespective of length $L$ whereas the entropy of free chain displays a pronounced minimum. At $chi^{c}$ all density profiles of absorbing chains with different $L$ intersect at the same distance from the grafting plane. The penetration/expulsion kinetics of free chains into the polymer brush after an instantaneous change in their compatibility $chi$ displays a rather rich behavior. We find three distinct regimes of penetration kinetics of free chains regarding the length $L$: I ($1le Lle 8$), II ($8 le L le N$), and III ($L > N$), in which the time of absorption $tau$ grows with $L$ at a different rate. During the initial stages of penetration into the brush one observes a power-law increase of $Gamma propto t^alpha$ with power $alpha propto -ln phi_o$ whereby penetration of the free chains into the brush gets {em slower} as their concentration rises.
